相关论文: Central limit theorem for anomalous scaling due to…

The Adaptive Multilevel Splitting algorithm is a very powerful and versatile iterative method to estimate the probability of rare events, based on an interacting particle systems. In an other article, in a so-called idealized setting, the…

A general formulation of translationally invariant, parametrically correlated random matrix ensembles, is used to classify universality in correlation functions. Surprisingly, the range of possible physical systems is bounded, and can be…

The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in presence of strong correlations between the added random contributions. Here, we study this problem for…

This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…

The central limit theorem provides the theoretical foundation for the universality of the normal distribution: under broad conditions, the asymptotic distribution of a sum of independent random variables approaches a Gaussian. Yet, physical…

Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at large argument of the probability density function of rescaled displacement (scaling function) is derived…

A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…

In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.

Using an averaged generating function for coloured hard-dimers, some random variables of interest are studied. The main result lies in the fact that all their probability distributions obey a central limit theorem.

In nature or societies, the power-law is present ubiquitously, and then it is important to investigate the mathematical characteristics of power-laws in the recent era of big data. In this paper we prove the superposition of non-identical…

We propose a simple model based on the Gnedenko limit theorem for simulation and studies of the ordinary Levy motion, that is, a random process, whose increments are independent and distributed with a stable probability law. We use the…

A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…

The global clustering coefficient serves as a powerful metric for the structural analysis and comparison of complex networks. Random geometric graphs offer a realistic framework for representing the spatial constraints and geometry often…

In classical diffusion, particle step-sizes have a Gaussian distribution. However, in superdiffusion, they have power-law tails, with transport dominated by rare, long L\'evy flights. Similarly, if the time interval between scattering…

A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…

Through certain appropriate constructions, we establish periodic solutions in distribution for some stochastic differential equations with infinite-dimensional Levy noise. Additionally, we obtain the corresponding periodic measures and…

In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is…

We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit distribution to be non-Gaussian. We note that the…

Standard continuous time random walk (CTRW) models are renewal processes in the sense that at each jump a new, independent pair of jump length and waiting time are chosen. Globally, anomalous diffusion emerges through action of the…